A Lumped-Parameter Model for Nonlinear Waves in Graphene

Hazim, Hamad; Wei, Dongming; Elgindi, M. B. M.; Soukiassian, Yeran

doi:10.4236/wjet.2015.32006

Cited by 5 publications

(10 citation statements)

References 8 publications

(6 reference statements)

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“…Through our results, we demonstrate that the second order material constant D is an important factor in modeling the patterns of graphene in vibrations and stability of electrostatic pull-in devices just as reported in [9] for mechanically operated devices [22].…”

Section: Introductionmentioning

confidence: 76%

“…Pull-in voltages are calculated for different areas of the plate at two different gap sizes. The analysis of phase diagrams demonstrates that, for high levels of the initial energy, some unknown behaviors of the solutions are discovered which are distinct from those found in [9] which only considers mechanically forced vibrations. Numerical solutions of some periodic waves have been presented and the values of periods and frequencies for three different values of length of the graphene are shown.…”

Section: Resultsmentioning

confidence: 99%

“…A nonlinear spring-mass model for electrostatically forced axial vibration of a graphene in a simple pull-in device is presented following the work of [9]. The existence of periodic solutions of free and forced vibrations is shown through phase plane analysis.…”

Section: Resultsmentioning

confidence: 99%

“…The goal of this work is to extend the results in [9] on this model for free and mechanically forced vibrations to the analysis of forced vibrations by considering the effect of the third-order stiffness constant as well as the electrostatic force. Through our results, we demonstrate that the second order material constant D is an important factor in modeling the patterns of graphene in vibrations and stability of electrostatic pull-in devices just as reported in [9] for mechanically operated devices [22].…”

Section: Introductionmentioning

confidence: 99%

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Periodic solutions of a graphene based model in micro-electro-mechanical pull-in device

Wei

Kadyrov

Kazbek

2017

ACM

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Phase plane analysis of the nonlinear spring-mass equation arising in modeling vibrations of a lumped mass attached to a graphene sheet with a fixed end is presented. The nonlinear lumped-mass model takes into account the nonlinear behavior of the graphene by including the third-order elastic stiffness constant and the nonlinear electrostatic force. Standard pull-in voltages are computed. Graphic phase diagrams are used to demonstrate the conclusions. The nonlinear wave forms and the associated resonance frequencies are computed and presented graphically to demonstrate the effects of the nonlinear stiffness constant comparing with the corresponding linear model. The existence of periodic solutions of the model is proved analytically for physically admissible periodic solutions, and conditions for bifurcation points on a parameter associated with the third-order elastic stiffness constant are determined.

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Section: Introductionmentioning

confidence: 76%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Periodic solutions of a graphene based model in micro-electro-mechanical pull-in device

Wei

Kadyrov

Kazbek

2017

ACM

Self Cite

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“…As is well-known, the field of modeling complex materials has been expanding rapidly in recent years, with the aim of understanding the dynamical response of metallic structures used in mechanical engineering applications. In this regard, I have been studying recently with Dr. Kostas Kaloudis and Dr. Thomas Oikonomou [34]1-D Hamiltonian lattices of particles interacting via 1) graphene type interactions [28][29][30], 2) Hollomon's power-law of materials exhibiting "work hardening" [31][32][33]. Earlier studies have focused on the dynamics of single oscillators governed by suitable nonanalytic potentials describing the motion in the above two cases.…”

Section: Future Outlookmentioning

confidence: 99%

Complex Dynamics and Statistics of 1-D Hamiltonian Lattices: Long Range Interactions and Supratransmission

Bountis

2020

Nonlinear Phenomena in Complex Systems

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In this paper, I review a number of results that my co-workers and I have obtained in the field of 1-Dimensional (1D) Hamiltonian lattices. This field has grown in recent years, due to its importance in revealing many phenomena that concern the occurrence of chaotic behavior in conservative physical systems with a high number of degrees of freedom. After the establishment of the Kolomogorov-Arnol'd-Moser (KAM) theory in the 1960s, a wealth of results were obtained about such systems as small perturbations of completely integrable Ndegree- of-freedom Hamiltonians, where ordered motion is dominant in the form of invariant tori. Since the 1980s, however, and particularly in the last two decades, there has been great progress in understanding the properties of Hamiltonian 1D lattices far from the KAM regime, where "weak" and "strong" forms of chaos begin to play an increasingly significant role. It is the purpose of this review to address and highlight some of these advances, in which the author has made several contributions concerning the dynamics and statistics of these lattices.

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Stability Properties of 1-Dimensional Hamiltonian Lattices with Nonanalytic Potentials

Bountis

Kaloudis

Oikonomou

et al. 2020

Int. J. Bifurcation Chaos

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We investigate the local and global dynamics of two 1-Dimensional (1D) Hamiltonian lattices whose inter-particle forces are derived from nonanalytic potentials. In particular, we study the dynamics of a model governed by a “graphene-type” force law and one inspired by Hollomon’s law describing “work-hardening” effects in certain elastic materials. Our main aim is to show that, although similarities with the analytic case exist, some of the local and global stability properties of nonanalytic potentials are very different than those encountered in systems with polynomial interactions, as in the case of 1D Fermi–Pasta–Ulam–Tsingou (FPUT) lattices. Our approach is to study the motion in the neighborhood of simple periodic orbits representing continuations of normal modes of the corresponding linear system, as the number of particles [Formula: see text] and the total energy [Formula: see text] are increased. We find that the graphene-type model is remarkably stable up to escape energy levels where breakdown is expected, while the Hollomon lattice never breaks, yet is unstable at low energies and only attains stability at energies where the harmonic force becomes dominant. We suggest that, since our results hold for large [Formula: see text], it would be interesting to study analogous phenomena in the continuum limit where 1D lattices become strings.

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A Lumped-Parameter Model for Nonlinear Waves in Graphene

Cited by 5 publications

References 8 publications

Periodic solutions of a graphene based model in micro-electro-mechanical pull-in device

Periodic solutions of a graphene based model in micro-electro-mechanical pull-in device

Complex Dynamics and Statistics of 1-D Hamiltonian Lattices: Long Range Interactions and Supratransmission

Stability Properties of 1-Dimensional Hamiltonian Lattices with Nonanalytic Potentials

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